Solving a system of equations by substitution involves expressing one variable in terms of the other in one equation, substituting this expression into the other equation, and solving for the variables. Verify the solution by checking in the original system.
Solving a system of equations by substitution involves expressing one variable in terms of the other in one equation and then substituting that expression into the other equation. Here's a step-by-step guide:
1. **Write Down the System:**
![\[ \begin{cases} ax + by = c \\ dx + ey = f \end{cases} \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/xm36w4bm5ojdkz74hpsg65qzfgmsbhc0pg.png)
2. **Choose an Equation:**
Select one of the equations to express one variable in terms of the other.
3. **Solve for a Variable:**
Solve the chosen equation for one variable (e.g., solve the first equation for \(x\) or \(y\)).
4. **Substitute:**
Substitute the expression obtained in step 3 into the other equation.
5. **Solve for the Second Variable:**
Solve the resulting equation for the second variable.
6. **Substitute Back:**
Substitute the found value into the expression obtained in step 3 to find the value of the first variable.
7. **Check:**
Verify the solution by substituting both values into the original system of equations.
This method helps find the values of the variables that satisfy both equations in the system.
The probable question may be:
How to solve system by substitution?